Prove Theorem 2.2.4 on page 73. In Theorem 2.2.4 Suppose that A1, A2, and B are events

Question:

Prove Theorem 2.2.4 on page 73.
In Theorem 2.2.4
Suppose that A1, A2, and B are events such that Pr(A1 ∩ B) > 0. Then A1 and A2 are conditionally independent given B if and only if Pr(A2|A1 ∩ B) = Pr(A2|B). This is another example of the claim we made earlier that every result we can prove has an analog conditional on an event B. The reader can prove this theorem in Exercise 22.